If a financial statement is accurate, ie the loans are properly classified and loss reserves are accurate, it gives a pretty good indication of the financial condition of a bank (or any company for that matter). I think the Vatican Bank should, as it intends to do, start publishing financial statements: accurate balance sheets, p/l statements, cash flows, etc. My interest in it is that there is no appearance of impropriety.
Having been involved for years with Diocesan, Parish, and Catholic school finances, I think you are wrong about it not being important for financial statements to be disclosed. There are lots of reasons for them to be so: donors want to know their money is being properly managed, having to publish financial statements helps enforce proper accounting procedures, it is way too easy for a finance committee/pastor/bishop to start making bad decisions (not necessarily dishonest) if they do not ever have to tell anyone the results, no one is going to feel comfortable long term in just treating the finances as a big, black box which only the finance committee can see into. And in the case of restricted assets, donors have a right to know that the money was spent on what they specified (and from experience, I can tell you that the mis-appropriation of restricted assets is the easiest error for financial managers of non-profits to fall into).
It is admirable that you would be willing to continue to support the Church financially just out of obligation, I feel the same, but there are limits.